In typical turbomachines, each row of aerofoil members divides a duct into a series of sectoral passages, each bounded by the opposed suction and pressure surfaces of a neighbouring pair of members and the radially inner and outer walls of the duct. The flow field within the sectoral passages is complex and includes a number of secondary vortical flows, which are a major source of energy loss. Reference can be made to Sieverding (1985) “Secondary Flows in Straight and Annular Turbine Cascades”, Thermodynamics and Fluids of Turbomachinery, NATO, Vol. 11, pp 621-624 for a detailed discussion of these flows. Their relative importance increases with increase of aerodynamic duty or decrease of aspect ratio. Not only is there energy dissipation in the secondary flows themselves, but they can also affect adversely the fluid flow downstream because they cause deviation of the exit angles of the flow from the row of aerofoil members.
The endwall boundary layers give rise to a substantial part of these secondary flows. FIG. 1 shows a flow model illustration taken from Takeishi et al (1989), “An Experimental Study of the Heat Transfer and Film Cooling on Low Aspect Ratio Turbine Nozzles” ASME Paper 89-GT-187. This shows part of a row of turbine blades projecting from a cylindrical surface that forms a radially inner endwall of the annular passage into which the blade aerofoil extends. The principal flow features as shown in the model are:
Rolling up of the inlet boundary layer L into a horseshoe vortex H at the blade leading edge due to the pressure variation at the intersection of the leading edge and the endwall. The pressure surface side leg of this flow becomes the core of a passage vortex P, which is a dominant part of the secondary flow. On the endwall, beneath the passage vortex, a new boundary layer is formed, indicated as crossflow B, which starts in the pressure side corner of the endwall of the blade passage.
Upstream of the crossflow B the inlet boundary layer is deflected across the passage, as indicated by crossflow A. The endwall separation line S marks the furthest penetration of the bottom of the inlet boundary layer A into the blade passage and divides it from the new boundary layer (crossflow B) forming downstream of it.
The new endwall boundary layer, crossflow B, continues onto the blade suction surface until it separates, along an aerofoil separation line V, and feeds into the passage vortex P. The horseshoe vortex suction side leg, referred to as the counter vortex U in the drawing, remains above the passage vortex P and moves away from the endwall as the passage vortex grows.
A small corner vortex C may be initiated in the corner region between the blade suction surface and the endwall, rotating in the opposite sense to the passage vortex.
Also illustrated in FIG. 1 are the attachment line T which represents the division of the incoming boundary layer flow L between adjacent passages, and the saddle point D, where the attachment line T and the endwall separation line S intersect.
Typically, the passage vortex will increase the exit angle of the flow at the endwall (referred to as “over turning”) with the compensatory reduction in exit angle away from the wall (referred to as “under turning”). These effects give rise to deviations of the inlet flow to the next aerofoil row, causing the angle of incidence of the flow on the aerofoils to vary positively or negatively from the design value and so reduce the aerodynamic efficiency of the flow.
There have been a number of proposals for reducing the secondary flows in the sectoral passages of a turbomachine.
Axisymmetric endwall profiling alters the endwall height by the same extent across the pitch. Axisymmetric geometries can affect the flow field, by causing local diffusion and accelerations independent of the aerofoil shape. The aim of changing the endwall shape by this means is usually related to achieving “area ruling”. The diffusion or acceleration does not have a direct impact on the formation of secondary flow structures.
U.S. Pat. No. 4,778,338 proposes a methodology for axisymmetric endwall profiling.
Non-axisymmetric endwall profiling alters the endwall height across the pitch, typically in addition to the axial direction. This freedom of design gives control over the static pressures near the endwall surface at any point in the passage. Rose, (1994), Non-axisymmetric Endwall Profiling in the HP NGVs of an Axial Flow Gas Turbine, ASME Paper No. 94-GT-249 demonstrates the effects of non-axisymmetric endwall profiling on the circumferential static pressure distribution at blade exit. The author also presents a CFD study where profiling is successfully used to reduce rim-seal leakage flows caused by non-uniform static pressures. Further studies of non-axisymmetric endwall profiling are reported by Hartland, Gregory-Smith and Rose, (1998), Non-Axisymmetric Endwall Profiling in a Turbine Rotor Blade, ASME Paper 98-GT-525; Harvey, Rose, Shahpar, Taylor, Hartland, and Gregory-Smith, Non-axisymmetric turbine endwall design: Part I. Three-dimensional design system, ASME J. Turbomachinery, 2000, 122, 278-285; and Hartland, Gregory-Smith, Harvey and Rose, (1999), Non-Axisymmetric Turbine Endwall Design: Part II Experimental Validation, ASME Paper 99-GT-338. Ingram, Gregory-Smith, Rose, Harvey, and Brennan, (2002), The effect of end-wall profiling on secondary flow and loss development in a turbine cascade, ASME paper GT2002-30339 provide a review of earlier work and explain that non-axisymmetric endwall profiling works by reducing the cross passage pressure gradient at the endwall by means of streamline curvature. The authors also note that the aim of their profiling designs was to reduce this cross passage gradient, which results in less secondary flow and therefore loss. Ingram, Gregory-Smith and Harvey, (2005), Investigation of a novel secondary flow feature in a turbine cascade with endwall profiling, Journal of turbomachinery transactions of the ASME 127(1): 209-214 discusses the limits of endwall profiling in terms of maximum values of perturbation magnitudes and endwall curvatures.
U.S. Pat. Nos. 3,529,631 and 6,283,713 propose forms of non-axisymmetric endwall profiling.